A Five-Level MILP Model for Flexible Transmission Network Planning Under Uncertainty: A Min–Max Regret Approach

The benefits of new transmission investment significantly depend on deployment patterns of renewable electricity generation that are characterized by severe uncertainty. In this context, this paper presents a novel methodology to solve the transmission expansion planning problem under generation expansion uncertainty in a min-max regret fashion, when considering flexible network options and $n-1$ security criterion. To do so, we propose a five-level mixed integer linear programming (MILP) based model that comprises: (i) the optimal network investment plan (including phase shifters), (ii) the realization of generation expansion, (iii) the co-optimization of energy and reserves given transmission and generation expansions, (iv) the realization of system outages, and (v) the decision on optimal post-contingency corrective control. In order to solve the five-level model, we present a cutting plane algorithm that ultimately identifies the optimal min-max regret flexible transmission plan in a finite number of steps. The numerical studies carried out demonstrate: (a) the significant benefits associated with flexible network investment options to hedge transmission expansion plans against generation expansion uncertainty and system outages, (b) strategic planning-under-uncertainty uncovers the full benefit of flexible options which may remain undetected under deterministic, perfect information methods, and (c) the computational scalability of the proposed approach.